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3 years ago

Find the value x in the triangle shown below.

Mathematics

2 answers:

cricket20 [7]3 years ago

7 0

Answer: A. Sqrt53

Explanation:

Use Pythagorean’s theorem to find hypotenuse:

A^2 + B^2 = C^2

7^2 + 2^2 = C^2

49 + 4 = C^2

53 = C^2

Sqrt53 = C

Svetlanka [38]3 years ago

4 0

Answer:c

Step-by-step explanation:

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Find sin 0, where is the angle shown. Give an exact value, not a decimal approximation.

Nata [24]

Answer:

$\displaystyle \sin\theta=\frac{12}{13}$

Step-by-step explanation:

Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:

$\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:

$a^2+b^2=c^2$

Let a be the adjacent side and b be the opposite side. c will be the hypotenuse.

Substitute:

$(5)^2+b^2=(13)^2$

Solve for b:

$b=\sqrt{169-25}=\sqrt{144}=12$

So, the opposite side measures 12.

Then sine will be:

$\displaystyle \sin\theta=\frac{12}{13}$

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IceJOKER [234]

Answer:

Step-by-step explanation:

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2 years ago

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The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

$S=4\pi r^2$

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

$\frac{d}{2}=r$ Now we can have the equation in terms of diameter instead of radius. Rewriting:

$S=4\pi(\frac{d}{2})^2$ which simplifies to

$S=4\pi(\frac{d^2}{4})$ and a bit more to

$S=\pi d^2$ (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

$\frac{dS}{dt}=\pi*2d\frac{dD}{dt}$ Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for $\frac{dD}{dt}$ , the rate at which the diameter is changing, when the diameter is 13. Filling in: